Competitive gene-set analysis tests whether the genes in a gene-set are more strongly associated with the phenotype of interest than other genes. To test this within the regression framework the model is first expanded to include all genes in the data. A binary indicator variable S s with elements s g is then defined, with s g = 1 for each gene g in gene set s and 0 otherwise. Adding S s as a predictor of Z yields the modelZ=β0s1→+Ssβs+ε. The parameter β s in this model reflects the difference in association between genes in the gene set and genes outside the gene set, and consequently testing the null hypothesis β s = 0 against the one-sided alternative β s > 0 provides a competitive test. Note that this is equivalent to a one-sided two-sample t-test comparing the mean association of gene-set genes with the mean association of genes not in the gene-set. Similarly, the self-contained analysis is equivalent to a one-sided single-sample t-test comparing the mean association of gene-set genes to 0.
